A problem in the volumetric medical image analysis is to characterize the 3D local structure of tumors across various scales, because the size and shape of tumors varies largely in practice. Such underlying scales of tumors also provide useful clinical information, correlating highly with probability of malignancy. There are a number of previously proposed approaches addressing this problem. However, these prior art approaches are prone to be sensitive to signal noises and their accuracy degrades when the target shapes differ largely from an isolated Gaussian. In the medical domain, these constraints are too strong since many tumors appear as irregular shapes within noisy background signals.